A Generalization of the Von Koch Curve

1965 ◽  
Vol 38 (3) ◽  
pp. 144 ◽  
Author(s):  
Joel E. Schneider
Keyword(s):  
Koch Curve ◽  
Von Koch Curve

FLIPPING COINS, FOLDING PAPER, AND FINDING FAMILIAR FRACTALS IN THE TOWER OF HANOI

Fractals ◽  
2009 ◽  
Vol 17 (01) ◽  
pp. 83-89
Author(s):  
DANE R. CAMP
Keyword(s):  
Koch Curve ◽  
Tower Of Hanoi ◽  
Paper Folding ◽  
Folding Paper ◽  
Coin Flipping ◽  
Von Koch Curve

This manuscript describes three activities connecting the Tower of Hanoi puzzle to three familiar fractal forms. The first connects coin flipping, paper folding, and the Tower of Hanoi to the Dragon Curve. The second illustrates mathematician Ian Stewart's method for showing how the relationships between possible states of the Tower of Hanoi are related to stages in Sierpinski's Gasket. The final activity compares right-left moves of Tower of Hanoi disks to iterations of the Von Koch Curve.

scholarly journals VON KOCH AND THUE-MORSE REVISITED

Fractals ◽  
2007 ◽  
Vol 15 (04) ◽  
pp. 405-409 ◽  
Author(s):  
J.-P. ALLOUCHE ◽  
G. SKORDEV
Keyword(s):  
Koch Curve ◽  
Automatic Sequences ◽  
Von Koch Curve

We revisit the relation between the von Koch curve and the Thue-Morse sequence given in a recent paper of Ma and Goldener by relating their study to papers written by Coquet and Dekking at the beginning of the 1980s. We also emphasize that more general links between fractal objects and automatic sequences can be found in the literature.

scholarly journals CALCULUS ON FRACTAL CURVES IN Rn

Fractals ◽  
2011 ◽  
Vol 19 (01) ◽  
pp. 15-27 ◽  
Author(s):  
ABHAY PARVATE ◽  
SEEMA SATIN ◽  
A. D. GANGAL
Keyword(s):  
Sobolev Spaces ◽  
Real Line ◽  
Mass Function ◽  
Koch Curve ◽  
Fractal Curve ◽  
Riemann Integral ◽  
The Real ◽  
Algorithmic Aspect ◽  
Ordinary Derivative ◽  
Von Koch Curve

A new calculus on fractal curves, such as the von Koch curve, is formulated. We define a Riemann-like integral along a fractal curve F, called Fα-integral, where α is the dimension of F. A derivative along the fractal curve called Fα-derivative, is also defined. The mass function, a measure-like algorithmic quantity on the curves, plays a central role in the formulation. An appropriate algorithm to calculate the mass function is presented to emphasize its algorithmic aspect. Several aspects of this calculus retain much of the simplicity of ordinary calculus. We establish a conjugacy between this calculus and ordinary calculus on the real line. The Fα-integral and Fα-derivative are shown to be conjugate to the Riemann integral and ordinary derivative respectively. In fact, they can thus be evalutated using the corresponding operators in ordinary calculus and conjugacy. Sobolev Spaces are constructed on F, and Fα-differentiability is generalized. Finally we touch upon an example of absorption along fractal paths, to illustrate the utility of the framework in model making.

A Generalization of the Von Koch Curve

1965 ◽  
Vol 38 (3) ◽  
pp. 144-147
Author(s):  
Joel E. Schneider
Keyword(s):  
Koch Curve ◽  
Von Koch Curve

Fractal Koch curve for UHF band application

2007 ◽  
Author(s):  
Mohd Nazri A. Karim ◽  
Mohamad Kamal A. Rahim ◽  
Mohamad Irfan ◽  
Thelaha Masri
Keyword(s):  
Koch Curve ◽  
Uhf Band

The Koch curve as a smooth manifold

2008 ◽  
Vol 38 (2) ◽  
pp. 334-338 ◽  
Author(s):  
Marcelo Epstein ◽  
Jędrzej Śniatycki
Keyword(s):  
Smooth Manifold ◽  
Koch Curve

scholarly journals Modified Koch Fractal Antenna for Multi and Wideband Wireless Applications

2021 ◽  
Vol 19 (2) ◽  
pp. 182-189
Author(s):  
Shweta Rani ◽  
Sushil Kakkar
Keyword(s):  
Numerical Simulations ◽  
Impedance Matching ◽  
Optimization Procedure ◽  
Design Parameters ◽  
Impedance Bandwidth ◽  
Fractal Antenna ◽  
Bacterial Foraging Optimization ◽  
Koch Curve ◽  
Wireless Applications ◽  
Koch Fractal

This paper focuses on the design and development of modified Koch fractal antenna. Compared to traditional Koch curve antenna, the presented antenna possesses a greater number of frequency bands and better impedance matching. Furthermore, the bacterial foraging optimization (BFO) approach is implemented to enhance the impedance bandwidth. The developed technique has been verified by employing various numerical simulations. The design parameters generated from the optimization procedure have been utilized to manufacture the antenna and the respective experimental and simulated results compared. The measured results show that the designed antenna exhibits multi and wideband behavior, covering WLAN, WIMAX, and various other wireless applications.

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